Veterans sizing up the men’s backgrounds said they did not see war experience as a factor in the attacks.

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Although both gunmen implicated in fatal ambushes of police officers in Dallas and Baton Rouge, Louisiana, were young military veterans, neither of the gunmen had combat experience, according to military records, and there is no evidence they suffered from post-traumatic stress disorder, or PTSD.

There is no data that suggests veterans as a whole are more likely to commit crimes. In fact, a number of veterans have noted that while both gunmen had served in the military, so had four of the eight officers who were killed, said Paul Rieckhoff, the founder and chief executive officer of the Iraq and Afghanistan Veterans of America.

“The truth is that veterans are much more likely to be the rescuer than the assailant,” said Rieckhoff, who was an Army infantry platoon leader during the invasions in Iraq. “But there is this lazy stereotype that we come back as damaged souls.”

Thousands of veterans have returned from Iraq and Afghanistan struggling to deal with their war experiences. And some research has shown that veterans with post-traumatic stress disorder are more likely to commit crimes.

Micah Johnson, who killed five police officers in Dallas this month, served in the Army Reserve from 2009 to 2015 as part of a construction platoon, and had only basic training with weapons.

Though he deployed to Afghanistan, nothing in his military record shows he saw combat, or that anyone in his unit was wounded. He acquired much of his tactical training outside the military.

Gavin Long, who killed three officers in Baton Rouge on Sunday, served in the Marine Corps from 2005 to 2010 as a data network specialist. He deployed to Iraq, but in a recent podcast, Long, using the name Cosmo, said he had not seen combat.

On Monday, veterans sizing up the men’s backgrounds said they did not see war experience as a factor in the attacks.

“Maybe there is something in the fact that they both served in the military, but it obviously doesn’t have anything to do with combat,” said Matt Gallagher, an Iraq war veteran and the author of the novel “Youngblood.” “The problem is the headlines don’t leave much room for nuance. The public sees veterans one of three ways: We are all heroes, we are all victims, or we are all monsters.”

A number of veterans’ groups, eager to cast off negative stereotypes, have banded together in recent years in an informal partnership they call the veterans’ empowerment movement. They organize volunteering trips and disaster relief teams, and exercise meetups to re-engage veterans in their communities. But, many say, negative stereotypes persist.

“We are seen as broken heroes,” said Bill Rausch, an Iraq war veteran who heads Got Your 6, a nonprofit that tries to improve portrayals of veterans in Hollywood and the media.

In a public survey the group conducted this year, he said, more than 80 percent of respondents said veterans suffered from mental health problems.

“Recent events only reinforce those perceptions,” he said. “If the American people are afraid of us instead of seeing us as an asset, it makes it more difficult for everyone.”